We study a strategy to manage demands that occur when an inventory system is temporarily out of stock: offer the customer facing the unsatisfied demand an economic incentive to backorder. We explore the benefits of this inventory management strategy by analyzing a model of an inventory system with stochastic demand and random supply disruptions, where the probability that a customer facing an unfilled demand will backorder (as opposed to becoming a lost sale) can be influenced by an economic incentive. Our results provide several insights regarding this inventory management strategy and suggest that the benefits of offering backorder incentives can be significant.